On the Capacity of the $K$-User Cyclic Gaussian Interference Channel

TL;DR

This paper analyzes the capacity of the $K$-user cyclic Gaussian interference channel, demonstrating that a Han-Kobayashi based strategy achieves near-optimal capacity within a constant gap in the weak interference regime and exploring the GDoF.

Contribution

It extends the Han-Kobayashi strategy to the $K$-user cyclic case, providing capacity bounds and GDoF analysis, with improved bounds for the 3-user case.

Findings

Achieves capacity to within 2 bits in the weak interference regime.

For the 3-user case, the gap is reduced to 1.5 bits with time-sharing.

GDoF of the symmetric cyclic channel matches the two-user case.

Abstract

This paper studies the capacity region of a $K$-user cyclic Gaussian interference channel, where the $k$th user interferes with only the $(k-1)$th user (mod $K$) in the network. Inspired by the work of Etkin, Tse and Wang, who derived a capacity region outer bound for the two-user Gaussian interference channel and proved that a simple Han-Kobayashi power splitting scheme can achieve to within one bit of the capacity region for all values of channel parameters, this paper shows that a similar strategy also achieves the capacity region of the $K$-user cyclic interference channel to within a constant gap in the weak interference regime. Specifically, for the $K$-user cyclic Gaussian interference channel, a compact representation of the Han-Kobayashi achievable rate region using Fourier-Motzkin elimination is first derived, a capacity region outer bound is then established. It is shown that the Etkin-Tse-Wang power splitting strategy gives a constant gap of at most 2 bits in the weak interference regime. For the special 3-user case, this gap can be sharpened to 1 1/2 bits by time-sharing of several different strategies. The capacity result of the $K$-user cyclic Gaussian interference channel in the strong interference regime is also given. Further, based on the capacity results, this paper studies the generalized degrees of freedom (GDoF) of the symmetric cyclic interference channel. It is shown that the GDoF of the symmetric capacity is the same as that of the classic two-user interference channel, no matter how many users are in the network.